User:Fitzgerald Lee/Edo Thirds: Difference between revisions

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added edos to 30
to 40
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|16||[[94edo|94]]||[[23/20]], 22/19, 7/6, 20/17, 19/16, 6/5, [[23/19]], 11/9, 16/13, 26/21, 5/4, [[19/15]], [[23/18]], 9/7, 22/17, [[30/23]]||||
|16||[[94edo|94]]||[[23/20]], 22/19, 7/6, 20/17, 19/16, 6/5, [[23/19]], 11/9, 16/13, 26/21, 5/4, [[19/15]], [[23/18]], 9/7, 22/17, [[30/23]]||||
|}
|}
This list could be used to get the minimal edos to add more flavours (of thirds).
{|class="wikitable"
{|class="wikitable"
!rowspan="1"|Edo!!rowspan="1"|[[23/20]]!!rowspan="1"|[[15/13]]!!rowspan="1"|[[22/19]]!!rowspan="1"|[[7/6]]!!rowspan="1"|[[20/17]]!!rowspan="1"|[[13/11]]!!rowspan="1"|[[19/16]]!!rowspan="1"|[[6/5]]!!rowspan="1"|[[23/19]]!!rowspan="1"|[[17/14]]!!rowspan="1"|[[28/23]]!!rowspan="1"|[[11/9]]!!rowspan="1"|[[16/13]]!!rowspan="1"|[[21/17]]!!rowspan="1"|[[26/21]]!!rowspan="1"|[[5/4]]!!rowspan="1"|[[24/19]]!!rowspan="1"|[[19/15]]!!rowspan="1"|[[14/11]]!!rowspan="1"|[[23/18]]!!rowspan="1"|[[9/7]]!!rowspan="1"|[[22/17]]!!rowspan="1"|[[13/10]]!!rowspan="1"|[[30/23]]
!rowspan="1"|Edo!!rowspan="1"|[[23/20]]!!rowspan="1"|[[15/13]]!!rowspan="1"|[[22/19]]!!rowspan="1"|[[7/6]]!!rowspan="1"|[[20/17]]!!rowspan="1"|[[13/11]]!!rowspan="1"|[[19/16]]!!rowspan="1"|[[6/5]]!!rowspan="1"|[[23/19]]!!rowspan="1"|[[17/14]]!!rowspan="1"|[[28/23]]!!rowspan="1"|[[11/9]]!!rowspan="1"|[[16/13]]!!rowspan="1"|[[21/17]]!!rowspan="1"|[[26/21]]!!rowspan="1"|[[5/4]]!!rowspan="1"|[[24/19]]!!rowspan="1"|[[19/15]]!!rowspan="1"|[[14/11]]!!rowspan="1"|[[23/18]]!!rowspan="1"|[[9/7]]!!rowspan="1"|[[22/17]]!!rowspan="1"|[[13/10]]!!rowspan="1"|[[30/23]]
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|[[31edo|31]]||||||||7||||||||8||||||||9||||||||10||||||11||||11|||||
|[[31edo|31]]||||||||7||||||||8||||||||9||||||||10||||||11||||11|||||
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|[[32edo|32]]||||||||||||||||||||||||||||||||||||||||||||||||
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|[[33edo|33]]||||||||||||||||||||||||||||||||||||||||||||||||
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|[[34edo|34]]||||||||||||||||9|| ||||||||||||||11|| ||||||||||||||
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|[[35edo|35]]||||||||8|| ||||||9|| ||||||||||||||11|| ||||||||||||||
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|[[36edo|36]]||||||||8|| ||||||9|| ||||||||||||||12|| ||||||||||||||
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|[[37edo|37]]||||||||8|| ||||||10|| ||||||||||||||12|| ||||||||||||||
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|[[38edo|38]]||||||||||||||||10|| ||||||||||||||12|| ||||||||||||||
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|[[39edo|39]]||||||||||||||||10|| ||||||||||||||13|| ||||||||||||||
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|[[40edo|40]]||||||||||||||||||||||||||||||||||||||||||||||||
|-
|-
|[[41edo|41]]||||8|| ||9|| ||10|| ||11|| ||||||12||12|| ||||13|| ||||14|| ||15|| ||16||
|[[41edo|41]]||||8|| ||9|| ||10|| ||11|| ||||||12||12|| ||||13|| ||||14|| ||15|| ||16||

Revision as of 02:37, 11 November 2025

First and second edos to have N number of thirds consistent in its odd limit (range is 15/13 to 13/10, closest JI interpretation that is consistent in the edo’s odd limit is shown):

Number of thirds First edo Thirds Second edo Thirds
0 1 None 2 None
1 3 5/4 4 6/5
2 5 7/6, 9/7 6 7/6, 5/4
3 15 7/6, 6/5, 5/4 18 7/6, 6/5, 5/4
4 19 7/6, 6/5, 5/4, 9/7 22 7/6, 6/5, 5/4, 9/7
5 26 7/6, 6/5, 16/13, 14/11, 13/10 (29) (~)
6 29 15/13, 13/11, 6/5, 16/13, 14/11, 13/10 (41) (~)
7 (41) (~) (58) (~)
8 (41) (~) (58) (~)
9 41 15/13, 7/6, 13/11, 6/5, 11/9, 5/4, 14/11, 9/7, 13/10 (58) (~)
10 58 15/13, 7/6, 13/11, 6/5, 17/14, 11/9, 5/4, 14/11, 9/7, 13/10 (72) (~)
11 72 15/13, 7/6, 20/17, 6/5, 17/14, 11/9, 16/13, 5/4, 14/11, 9/7, 22/17 (80) (~)
12 (80) (~) (94) (~)
13 80 22/19, 7/6, 20/17, 19/16, 6/5, 17/14, 11/9, 16/13, 5/4, 24/19, 14/11, 9/7, 22/17 (94) (~)
14 (94) (~)
15 (94) (~)
16 94 23/20, 22/19, 7/6, 20/17, 19/16, 6/5, 23/19, 11/9, 16/13, 26/21, 5/4, 19/15, 23/18, 9/7, 22/17, 30/23
Edo 23/20 15/13 22/19 7/6 20/17 13/11 19/16 6/5 23/19 17/14 28/23 11/9 16/13 21/17 26/21 5/4 24/19 19/15 14/11 23/18 9/7 22/17 13/10 30/23
1
2
3 1 1
4 1 1 1
5 1 1 2 2
6 1 2 2
7 2 2
8 2 3
9 2 2 3
10 2 3 3
11
12 3 3 4 4
13
14
15 3 4 5
16 4 4 5
17
18 4 5 6
19 4 5 6 7
20
21
22 5 6 6 7 8
23 6 7
24 6 8
25 7 8
26 6 6 7 8 8 8 9 9 10
27 6 7 9 10
28 7 9
29 6 6 7 8 8 9 9 10 11 11
30
31 7 8 9 10 11 11
32
33
34 9 11
35 8 9 11
36 8 9 12
37 8 10 12
38 10 12
39 10 13
40
41 8 9 10 11 12 12 13 14 15 16
58 12 13 14 14 15 16 17 17 19 20 21 22
72 15 16 17 17 19 20 21 22 23 25 26 27
80 17 17 18 19 19 20 21 22 23 24 26 27 27 28 29 30 30
94 19 19 20 21 22 23 23 25 26 26 27 27 28 29 29 30 32 32 33 33 34 35 36 36
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